(复杂)网络涉及到一个基础的信息分享问题，即网络节点之间通过信息分享与融合，最终达成“一致”/Consensus，及网络一致性。特别是相比于基于含有一个网络中间节点的中心式/Centralized网络，分布式网络中只通过节点与节点连接（相互称为邻居节点）进行通信，而没有中心节点，所以网络结构更为稳定（不会因为某一节点的破坏等而造成网络瘫痪），易于扩展（网络节点的性质一致，所以任何节点都可以再增加邻居节点）等，也实际上是很多物理网络（如监控传感网、社交网络等）的本质特征。

然而，在多目标跟踪多传感器信息融合里面却存在一个有趣的发现：传感器邻居节点相互之间分享的信息并不一定越多对于大家越有利，这里的“利”特指提高传感器节点估计的精度。这一点初感违背我们的直觉，因为一般的来讲：信息越多（应该）越有利。

那么为什么呐？ 物理传感器往往都遭受两类问题：一类是漏检，一类是虚警。前者是传感器没能获得目标的观测数据所造成，即missingdata问题。而后者是传感器遭遇干扰，获得观测数据不属于任何目标，是假信号，即falsedata问题。如此情况下，一个直观的逻辑是：因为有些信号可能是falsedata相关，其对于邻居节点没有益处，反而可能造成误导。因此，信息的分享就不见得越多越好，

这一现象可称之为：Many Could Be Better Than All，或者Less-is-More。实际这一现象并不罕见，如在认知科学/cognitive science（Gigerenzer, G., Brighton, H., 2009. Homo heuristicus: Why biased minds make better inferences. Topics in Cognitive Science, 1(1):107–143.）和神经网络/neural networks（Zhi-Hua Zhou, Jianxin Wu, Wei Tang, Ensembling neural networks: Many could be better than all, In Artificial Intelligence, Vol. 137, Issues 1–2, 2002, Pages 239-263。）都有所表现。

因此适当的控制信息分享量（更宽泛的是，只分享有利的信息，而尽量减少误导性或者干扰性的信息），不但显然有利于降低通讯开支（这一点在现实中往往很重要，甚至是网络的重要限制。特别是分布式传感器网络往往都是low-powered/低耗的传感器构成，以减少通讯和造价开支等）, 反而还可能更利于获得更高估计精度。

下文基于高斯混合实现PHD滤波进行杂波环境下的多目标探测与估计揭示这一发现，提出了“部分一致性”Partial Consensus的概念：（达成）部分一致要优于(达成)完全一致。同时在随机集PHD一致性信息融合方式上给出了一些探索性思考，特别明确和比较了（简单却被忽视的）算术平均Arithmetic Average和（当前主流）几何平均Geometric Average的区别和相对优势。

• T. Li, J.M. Corchado and S. Sun, Partial Consensus and Conservative Fusion of Gaussian Mixtures for Distributed PHD Fusion, IEEE Trans. Aeros. Electr. Syst., 2018, DOI: 10.1109/TAES.2018.2882960.  IEEE Xplore

连接：

Partial Consensus and Conservative Fusion of Gaussian Mixtures for Distributed PHD Fusion

Tiancheng Li ; Juan M. Corchado ; Shudong Sun

IEEE Transactions on Aerospace and Electronic Systems

Abstract:

We propose a novel consensus notion, called "partial consensus", for distributed Gaussian mixture probability hypothesis density fusion based on a decentralized sensor network, in which only highly-weighted Gaussian components (GCs) are exchanged and fused across neighbor sensors. It is shown that this does not only gain high efficiency in both network communication and fusion computation but also significantly compensates the effects of clutter and missed detections. Two "conservative" mixture reduction schemes are devised for refining the combined GCs. One is given by pairwise averaging GCs between sensors based on Hungarian assignment and the other merges close GCs for trace-minimal yet conservative covariance. The close connection of the result to the two approaches, known as covariance union and arithmetic averaging, is unveiled. Simulations based on a sensor network consisting of both linear and nonlinear sensors have demonstrated the advantage of our approaches over the generalized covariance intersection approach.

相关连接：

研究进一步扩展到采用随机样本（粒子滤波器）实现后验分布下的分布式“部分一致性”PHD滤波。

A Distributed Particle-PHD Filter with Arithmetic-Average PHD Fusion

Tiancheng Li, Franz Hlawatsch

(Submitted on 17 Dec 2017 (v1), last revised 20 Dec 2018 (this version, v2))

We propose a particle-based distributed PHD filter for tracking an unknown, time-varying number of targets. To reduce communication, the local PHD filters at neighboring sensors communicate Gaussian mixture (GM) parameters. In contrast to most existing distributed PHD filters, our filter employs an `arithmetic average' fusion. For particles--GM conversion, we use a method that avoids particle clustering and enables a significance-based pruning of the GM components. For GM--particles conversion, we develop an importance sampling based method that enables a parallelization of filtering and dissemination/fusion operations. The proposed distributed particle-PHD filter is able to integrate GM-based local PHD filters. Simulations demonstrate the excellent performance and small communication and computation requirements of our filter.

研究进一步扩展到测距受限传感网下的多目标跟踪： 

Local-Diffusion-based Distributed SMC-PHD Filtering Using Sensors with Limited Sensing Range

Tiancheng Li ; Víctor Elvira ; Hongqi Fan ; Juan M. Corchado

IEEE Sensors Journal

Abstract:

We investigate the problem of distributed multitarget tracking by using a set of spatially dispersed, collaborative sensors with limited sensing range (LSR), where each sensor runs a sequential Monte Carlo-probability hypothesis density filter and exchanges relevant posterior information with its neighbors. The key challenge stems from the LSR of neighbor sensors whose fields of view (FoVs) are partially/non-overlapped and therefore they may observe different targets at the same time. With regard to the local common FoVs among neighbor sensors, the proposed distributed fusion scheme, called local diffusion, performs one iteration of neighbor communication per filtering step in either of two means. One is given by immediate particle exchange, in which a reject-control operation is devised to reduce the number of communicating particles. The other is done by converting the particle distribution to Gaussian functions for parametric information exchange and fusion. The performance of both approaches has been experimentally investigated via simulation for different LSR situations and compared with cutting-edge approaches.